Problem: Simplify the following expression: $\sqrt{90} + \sqrt{40}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{90} + \sqrt{40}$ $= \sqrt{9 \cdot 10} + \sqrt{4 \cdot 10}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{10} + \sqrt{4} \cdot \sqrt{10}$ $= 3\sqrt{10} + 2\sqrt{10}$ Finally, simplify by combining the terms. $= ( 3 + 2 )\sqrt{10} = 5\sqrt{10}$